Timeline for Improving a sequence of 1s and -1s
Current License: CC BY-SA 2.5
11 events
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| Apr 16, 2010 at 18:58 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Apr 16, 2010 at 17:07 | comment | added | Ian Morris | The example gowers is looking for is given in the last few pages of "Ergodic sets" by Oxtoby (BAMS 1952). | |
| Jan 17, 2010 at 22:02 | comment | added | Anton Petrunin | @Joe. There is no "significance" :) I only want to say that quasiperiodicity is maximum structure one can extract. (Maybe I did not understand your question.) | |
| Jan 17, 2010 at 18:31 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Jan 17, 2010 at 17:37 | comment | added | Joel David Hamkins | @Anton. Thanks. I had understood that you can go back, but didn't see at first the full significance of this. It shows, for example, that you can't get an actually periodic limit. | |
| Jan 16, 2010 at 5:32 | comment | added | Anton Petrunin | @Joel, I assume you mean my P.S. --- Simply use the def. of quasiperiodic sequence. Let $A$ be the old (infinite) sequence and $B$ is the new one. Note that any sequence of length $\ell$ in $A$ can be found in the any sequence of length $L(\ell)$ of $B$. Choose bigger and bigger nbhds of zero in $A$ and shift $B$ to move corresponding piece back to zero-position, then pass to the limit. | |
| Jan 16, 2010 at 4:13 | comment | added | Joel David Hamkins | I understand Gowers's simple lemma and (his "I think" remark) that it implies that you can reach a quasiperiodic limit, but could you explain your "but you will not get more" remark? | |
| Jan 15, 2010 at 18:19 | comment | added | Anton Petrunin | NO --- to construct an example, choose $L$ which grows very fast. | |
| Jan 15, 2010 at 15:44 | comment | added | gowers | Quick question: does the set of 1s in a quasiperiodic sequence have to have a well-defined density? I keep trying to find a counterexample and I keep failing. | |
| Jan 15, 2010 at 14:28 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Jan 15, 2010 at 14:20 | history | answered | Anton Petrunin | CC BY-SA 2.5 |